Part of being a competent speaker of a language is being "properly attuned" to logical relations between sentences in the language. A question of foundational interest in semantics is: Which logical relations are relevant to the study of linguistic meaning, and how should they be characterized? Furthermore, what does it mean to be "properly attuned" to such relations? I will present two case studies based on my recent work that bear on these questions: the first on so called probability operators such as 'probably' and 'at least as likely as'; the second on "surface level" inference patterns that are easily detectable and closely associated with grammatical phenomena. Connections to psychology of reasoning and computational linguistics will also be discussed.